A solution in closed form and a series solution to replace the tables for the thickness of the equivalent layer in Hooghoudt's drain spacing formula

In this article, a new analytical technique called Improved Parker-Sochacki Method (IPSM) for solving nonlinear Michaelis-Menten enzyme catalyzed reaction model is proposed. The global form of the solution for the concentrations of the substrate, enzyme and the enyzme-free product are obtained. Employing the Laplace-Pade resummation as a post processing technique on the computed series solution, the domain of convergence of the solution is greatly extended. The solution is therefore devoid of limited convergence interval that is typical of series solution of nonlinear differential equations. The proposed method showed a significant improvement over the conventional Parker-Sochacki Method (PSM). Furthermore, comparison of the results with numerically computed solutions elucidated the simplicity and accuracy of the proposed method.

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Scattering of waves by a half-screen with different face impedances: closed form series solution

International Journal of Electronics ◽

10.1080/00207217.2012.727351 ◽

2013 ◽

Vol 100 (7) ◽

pp. 928-941

Author(s):

Yusuf Z. Umul

Keyword(s):

Closed Form ◽

Series Solution

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Macroapproach Closed-Form Series Solution for Orthotropic Plates

Journal of Structural Engineering ◽

10.1061/(asce)0733-9445(1995)121:3(420) ◽

1995 ◽

Vol 121 (3) ◽

pp. 420-432 ◽

Cited By ~ 2

Author(s):

Roberto Lopez-Anido ◽

Hota V. S. GangaRao

Keyword(s):

Closed Form ◽

Series Solution ◽

Orthotropic Plates

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Exact deflection expressions for a thin solid circular plate loaded by periphery couples

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1243/0954406011520751 ◽

2001 ◽

Vol 215 (3) ◽

pp. 341-351 ◽

Cited By ~ 3

Author(s):

A Nobili ◽

A Strozzi ◽

P Vaccari

Keyword(s):

Closed Form ◽

Circular Plate ◽

Series Solution ◽

Analytical Form ◽

Mechanical Analysis ◽

Boundary Line ◽

Plate Edge ◽

Line Load ◽

Title Problem ◽

Radial Axis

A mechanical analysis is carried out for a thin, solid, circular plate, deflected by a series of periphery-concentrated couples with a radial or circumferential axis. Although such couples need not be of equal intensity or angularly equispaced, they must constitute a self-equilibrated system of couples. This problem is decomposed into a combination of two basic models, the first of which considers a single periphery couple with a radial axis, and the second addresses an edge couple with a circumferential axis. In both models the concentrated border couple is equilibrated by a sinusoidal boundary line load of proper intensity, whose wavelength equals the plate edge. When such basic configurations are combined, respecting the condition that the system of concentrated couples be self-equilibrated, the effects of the sinusoidal loads cancel out, and the title problem is recovered. A classical series solution in terms of purely flexural plate deflections is achieved for the two basic models, where the series coefficients are computed with the aid of an algebraic manipulator. For both models, the series is summed in analytical form over the whole plate region. Closed-form deflection formulae can thus be easily derived from the two basic models for any combination of self-equilibrated edge couples, where some selected relevant situations are developed in detail.

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